This often comes up in discussions pitting the US against the EU countries.

I'm not familiar with all of them, but here in "free, socialized healthcare" France, if you don't have a "mutuelle", which seems similar to "employer-dependant healthcare" in the US, you're going to have to pay out of pocket quite a lot of money. Maybe not as much as in the US (not familiar with that country), but very much not free. Think dental, glasses, needing to spend a night in a hospital for whatever reason (even public ones!), etc. On top of your salary being much lower.

Sure, you don't need an employer to have a mutuelle, you can pay for your own. But it's usually pricier and worse coverage.